Pure Mathematics

There is no way to guarantee in advance what pure mathematics will later find application. We can only let the process of curiosity and abstraction take place, let mathematicians obsessively take results to their logical extremes, leaving relevance far behind, and wait to see which topics turn out to be extremely useful. If not, when the challenges of the future arrive, we won’t have the right piece of seemingly pointless mathematics to hand.

Mathematical development in England was at a low ebb in the early decades of the nineteenth century, with Cambridge stagnating in the shadow of Newton, who had produced his mathematics nearly a century and a half earlier. This dead hand of tradition, which stifled much initiative and originality, was in sharp contrast to the situation in France.

Pure mathematics is, in its way, the poetry of logical ideas.  One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships.  In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.